Most definitely there are full-time and part-time parents.
I don't consider any mother or father that works but still loves, takes care of, spends time with, etc.. their children a part-time parent.
But, for example, Robert.. my ex.. I consider him a part-time parent and he even tells me that he only wants her sometimes when he feels like it. He doesn't miss her all of the time. He takes her for like 3-4hours a week.. maybe less and besides that, could care less how she is doing, never calls nor asks. That, to me, is a part-time parent. I work PT, go to school FT, and I consider myself a "home-maker" as well and I would smack someone if they said I wasn't a full-time mother because I'm not home 24/7.

Another example.. My friend's cousin leaves her kids with his parents (so.. his cousin's aunt and uncle) with her kids for MONTHS at a time. She leaves the middle child with them every year for 5 years for about 5-6months at a time. Now, she has a 3 year old and they have kept him on and off for a year.. The longest stretch being 5 months. And.. she doesn't call nor stop by when she drops them off. They are supposed to stay for the weekend and end up there for months. A total part-time mom.. if its not his parents, its his grandparents or someone else with the kids.. she never keeps them for more than 2-4 weeks at a time.